Religions 2020, 11, 102; doi:10.3390/rel11030102 www.mdpi.com/journal/religions
How Accurately Could Early (622-900 C.E.) Muslims
Determine the Direction of Prayers (Qibla)?
Walter R. Schumm
School of Family Studies and Human Services, College of Health and Human Sciences,
Kansas State University, 1700 Anderson Avenue, Manhattan, KS 66506-1403, USA; firstname.lastname@example.org
Received: 20 December 2019; Accepted: 20 February 2020; Published: 25 February 2020
Abstract: Debate has arisen over the ability of Muslim architects in the first two centuries of Islam
to determine true qiblas accurately. Some believe that they had such a capability, while others think
not. The argument could be more complex—perhaps some architects could, while others could not;
perhaps their accuracy changed over time or over greater distances from qibla targets. Here, we
investigated how the accurate qiblas of 60 mosques or related structures were, using data from
Daniel Gibson’s books and websites. Contrasts were drawn between theories that the qiblas of
early mosques were—or were not—generally accurate. If one were to assume that Mecca was the
only qibla, qiblas would not appear to have been accurate. However, if one were to assume that
qiblas changed, it would be found that qiblas were accurate to plus or minus two degrees in over
half of the cases and accurate within plus or minus five degrees in over 80% of cases. Accuracy was
not related to distance but did appear to improve over historical time, while distance from the
target cities and historical time were positively associated. The average qibla accuracy had a near
zero error, with random variations on either side of that zero error. The overall distribution was not
normal—kurtotic—because a greater accuracy was found than would have been expected with a
normal distribution; however, the pattern deviated more from a uniform distribution than it did
from a normal distribution. To try to synthesize the competing theories, we analyzed data for only
14 of the 60 mosques, those presumed to face towards Mecca, and we found fairly high degrees of
qibla accuracy with nearly 43% of qiblas within two degrees of accuracy and nearly 80% within five
degrees of accuracy. Comparing the accuracy of Meccan qiblas with other qiblas of the same
century, we found no significant differences in azimuth errors. While some architects were more
accurate than others, early Muslim architects seemed, in general, quite capable of placing qiblas
with reasonable accuracy, even though their accuracy may have improved slightly over the first
two centuries of Islam.
Keywords: Islam; qibla; Dan Gibson; early Islamic history; statistics and religion
Architecture is closely tied to religion, even in our modern age (de Wildt et al. 2019). For
thousands of years, faithful Sunni Muslims have dutifully prayed toward the holy city of Mecca five
times a day (Shia, three times a day). Ilci et al. (2018) have reported that “Facing towards the qibla….
is one of the six conditions or requisites of the prayer for being valid. In other words, if a person does
not turn his/her face to the qibla direction within an acceptable declination, his/her prayer is invalid
according to scholarly consensus” (p. 1642). However, could early Muslims in the first two or three
centuries of Islam accurately determine the qibla? Brubaker (2019, p. 17) has mentioned the work of
Dan Gibson, who claims that Mecca was not the original holy city of Islam, although Brubaker does
not take a firm position on that claim. However, Petersen (1996) has stated that “Many early
mosques were not built to a correct qibla orientation…” (p. 240). King (1990) acknowledges that
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many early mosques did not face toward Mecca, the city (p. 246). That might imply that qiblas were
not able to be measured accurately, which is an empirical rather than philosophical question, a
question that can be investigated scientifically. The point of contention is not that some early
mosques do not appear to point toward the city of Mecca (most scholars seem to agree on that) but
on how to explain that issue, especially with respect to technological limitations at that earlier time.
As Brubaker (2019) noted, Dan Gibson (2011; 2017) has created considerable controversy over
his claim that “Islam’s first Holy City was Petra, not Mecca” (Lecker 2014, p. 465). Oakes (2015), after
reviewing Gibson (2011), invites a response to Gibson, saying “Gibson’s evidence is just begging for
a response” (p. 426), echoing Waugh’s (2012, p. 201) similar earlier comment that the qiblas of the
earliest mosques did not seem to consistently face Mecca, an issue “which surely begs for
explanation”. Indeed, there have been responses to Gibson and to earlier scholars who also argued
against Mecca as the first holy city. Countering such assertions are many others (Saifullah, Ghoniem,
Al-Rahman, Squires, and Ahmed, 2001; King 1993). For example, Saifullah et al. (2001) argued that
“A small, defiant, and largely discredited group of Orientalists have argued that the early mosques
were not oriented toward Makkah…. a theory that challenges the Muslim belief that the earliest
mosques were directed toward the K’abah” (p. 1). Furthermore, Saifullah et al. (2001) argued that
during the beginning of Islam “the tools for accurately determining the direction were not available
at all” (p. 15). Later they claim that determining the qibla in early mosques was “as one can easily
see, was only a rough guess” (p. 17). They conclude that “In the early centuries of Islam, Muslim[s]
did not have tools to determine the qibla with precision” (p. 19). Similarly, Ilci et al. (2018) stated that
“During the first two centuries of Islam, when mosques were being built in different geographic
locations, Muslims did not have sufficient scientific background to find the direction of qibla” (p.
1643). For his part, David King (2018–2019) takes issue with Gibson’s ideas, noting in various places
that Gibson is an “amateur” (p. 347) and his documents “non-scholarly” (p. 347). His work is “an
insult to Muslim and Western scholarship” (p. 347). King claims that Gibson’s text (2017) “is of the
kind one would expect from a first-year college student” (p. 349). Rather, King argues that “Muslims
for the first two centuries used folk astronomy, particularly astronomical horizon phenomena, the
cardinal directions and solar risings and settings at the solstices; the reason they did this was
because the Ka’ba itself is astronomically aligned and they wanted to face an edifice, the Ka’ba, not
the town of Mecca” (p. 349). Furthermore, King has argued that “the earliest Muslims could never
have aligned mosques accurately toward the modern direction of Petra, or, for that matter, toward
the modern direction of Mecca either” (p. 351). More specifically, he argues that “the first
generations of Muslims had no means whatsoever for finding the direction of Petra accurately to
within a degree or two, not the least because they had no access to any geographical coordinates, let
alone modern ones, and no mathematics whatsoever” (p. 354). In a different article, King (1990)
argues that “In the first two centuries of Islam, when mosques were being built from Andalusia to
Central Asia, the Muslims had no truly scientific means of finding the qibla” (p. 253). Anderson
(2018) agrees, stating that “Hence, the only explanation for any early mosques accurately oriented
toward either Petra or Mecca—if indeed any exist—is coincidence.” Instead, King argues that many
mosques simply faced south or in some other direction (rising summer or setting winter sun) or tried
to align with the axis of the Ka’ba. King concludes that we need to “identify the diverse ways that
were used for finding the qibla in each location” (p. 361) and that Gibson’s ideas are “complete
nonsense” (p. 363), even though “His followers will surely believe everything he writes” (p. 366). In
another paper, King (2018) argues that Gibson “has no qualifications”, “no understanding”, “seems
oblivious”, “has erred monumentally”, and has reached “false conclusions” (p. 9). Elsewhere, King
(2018) has asserted that Gibson’s “crackpot theories” are “crazy and potentially dangerous” (p. 26).
I tend to become uneasy when I observe ad hominem attacks on scholars with whom one may
differ, especially when a person is labeled “discredited” without specific evidence. However, good
science (and history) depends on good measurement, sound reasoning, and effective statistical
methodology. It is one thing to claim something, another entirely to provide systematic and
scientific/statistical evidence for that claim. As Lecker (2014, p. 467) has noted, a qibla towards Petra
might also be one directed towards Jerusalem, so the ability of architects in ancient Islam to
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determine their direction of prayer accurately enough to distinguish between nearby target cities
remains an open question (King 1986). Ordinary lay persons might question the ability of ancients to
be able to determine qiblas, or the directions of prayer to holy cities accurately, as they lacked so
much of the technology available to us today. As noted, King, Anderson, and presumably many
other scholars would agree.
Such controversies are occurring, of course, in a contentious background in which some
political interests in the West have been ideologically attacking and denigrating Muslims and Islam,
possibly out of fear and their own insecurities (Sharify-Funk 2013), a process with a long history
(Firestone 2019; Ismail and Mat 2016). Naturally, Muslims resent such attacks and have vigorously
analyzed them and defended against them (Bazian 2018; Haddad and Harb 2014; Khan et al. 2019;
Larsson 2012; Mohammed 2018). Although some may see science and statistics as a tool of the
oppressor who wants to merely “display” objectivity [falsely] (Khan et al. 2019, p. 7, point number
20), I prefer to see science and statistics as a way to at least partially control for bias and to improve
objectivity if done well, even though I also recognize that research can be distorted to conform to
political objectives (Schumm 2015; Schumm and Crawford 2020). In other words, I agree with
Sharify-Funk (2013), who recognized that “critical examination is needed” (p. 465) when dealing
with emotionally charged issues. The use of statistics is one way to critically examine arguments that
can be discussed in terms of specific data points.
It seems to this author that Gibson deserves a better response (Oakes 2015) than ad hominem
attacks. What about a scientific, statistical analysis of his claims? The main objective here is to
provide the first statistical analysis of his data. Even if we do not understand exactly how the
ancients might have been able to determine an accurate direction to a distant holy city, it may be
possible to determine to what extent they were successful in doing so. Having some idea of their
degree of accuracy would seem to be a pre-requisite to determining if they could distinguish
between cities (e.g., Jerusalem versus Mecca). In this paper, I want to assess the potential accuracy of
ancient Islamic qiblas. Our source of data will be limited to data provided by Gibson in his books
(2011, 2017) and his website, using his most recent data wherever possible. Gibson has provided the
azimuths between different mosques or other Islamic structures and target locations, such as Mecca.
He has also provided, for each mosque or structure, the degree of error in the azimuth. For example,
if Mecca was distant by 45 degrees but the mosque’s direction of prayer was aimed at 50 degrees,
then it would require backing off 5 degrees to get to a correct azimuth (i.e., an error of −5 degrees).
Lacking alternative sources of data, I will rely cautiously on data from Gibson. The primary goal is to
apply statistics to determine the apparent degree of accuracy of ancient Islamic qiblas on a cautious
assumption that Gibson’s data were valid. However, I also wished to determine if the accuracy of
qiblas was a function of an approximate distance from the target holy city or of the approximate date
of construction of the buildings.
3. Methods and Procedures
The accuracy of a qibla depends on its target. Gibson’s thesis is that the targets changed from
Petra to a site between Petra and Mecca and then to Mecca. The anti-thesis of King and others is that
Mecca was the proper site all along. First, we will test our hypotheses under Gibson’s assumptions,
then under King’s assumption. Finally, we will attempt something of a synthesis of the competing
ideas, using data which both Gibson and King might agree represented the same qibla target, what
some scientists might call a “critical test” of the competing theories. Other scholars are welcome to
try other approaches to comparing the theories of Gibson versus King and apply statistical testing to
determine which theories better fit their data. We would prefer that to further ad hominem attacks.
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For many ancient structures, neither the date of construction or the original floor plan (and
hence, qibla) can be determined with precision. There are numerous mosques whose original qiblas
or dates cannot be determined and, thus, were not used in our analyses (Table 1). I eliminated
structures from consideration if their date of construction was not known because it hindered our
assessment of our fifth hypothesis (below) or if the estimated date of construction was before 622
C.E. or after 900 C.E. (Table 1). I also eliminated structures from consideration if their qiblas did not
appear to target any particular city but seemed to aim to the southeast from places in the western
Mediterranean area [Gibson (2017) argues they were paralleling a line drawn from Petra to Mecca;
others might think they were paralleling the long axis of the Ka’ba; Daniel Gibson (personal
communication, 14 December 2019) also thinks the long axis of the Ka’ba points northwest towards
Petra, where he claims the original Ka’ba was located]. Mosques for whom the best qibla was in
error by more than 20 degrees were eliminated, as outliers (Table 1), from consideration. I did
include Cheramin Juma (Gibson 2017) in the analyses, although on his site Gibson lists it as
unknown. After eliminating ineligible structures, there were 60 left as of February 2020 (Table 2).
Table 1. Mosques not included in analyses with explanations.
Name of Mosque/Site Date
(C.E.) Location A B C D E F G
Quba Mosque 622 Medina, Saudi Arabia X
Prophet’s Mosque 623 Medina, Saudi Arabia X
Mosque of the Two Qiblas 626 Medina, Saudi Arabia X
anad Mosque 627
anad, Yemen X
Jowatha Mosque 629 Al-Kilabiyah, Saudi
Umar ibn al-Khattab Mosque 634 Dawmat al Jandal,
Saudi Arabia X
Mosque of the Prophet Jonah 637 Mosul, Iraq X
Kufa Grand Mosque 638 Kufa, Iraq X
Ugba Ibn Nafi Mosque 640 Kairoun, Tunisia X
Hala Sultan Tekke 649 Larnaca, Cyprus X
Iman Shafi’l Mosque 649
eddah, Saudi Arabia X
Mosque of Sidi ‘Ukba 686 Biskra, Algeria X
Dome of the Rock 690 Jerusalem X
Qasr Burqu’ 700 Jordan desert X
Masjid al Khamis 717 Manama, Bahrein X
Mosque of Rusafa 724 Baghdad, Iraq X
Grand Hussein Mosque 725 Amman, Jordan X
Huajuexiang Mosque 742 Xian, China X
Amra Bathhouse 743 Jordan desert X
Shibam Palace 753 Shibam, Yemen X
Masjid al Jami Grand Mosque 772 Ishfan, Iran X
Qasr Uweinid 8th C.
ordan desert X
Erbil Grand Mosque 8th C. Erbil, Iraq X
Be’er Ora Qiblatain Mosque 8th C. Be’er Ora, Israel X
Fenghuang Mosque 8th C. Hangzhou, China X
ob’s Tomb Shrine 8th C. Salalah, Oman X
Al-Asha’ir Mosque 820 Zabid, Yemen X
Grand Mosque of Shibam 871 Shibam, Yemen X
Sidi Ghanem Mosque 678 Mila, Algeria X
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Graveyard of Sidi Ukba 686 Biskra, Algeria X
Jami’ al-Zaytuna 732 Tunis, Tunisia X
Ribat Fortress 770 Ribat, Tunisia X
Tauste Graveyard 772 Zaragoza, Spain X
Cordoba Mosque 784 Cordoba, Spain X
Shrine of Kazmiyya 799 Baghdad, Iraq X
Dougga Mosque 800 Dougga, Tunisia X
Rand Mosque of Kairoun 817 Kairoun, Tunisia X
Moulay Idriss, II Tomb and
Mosque 828 Fex, Morocco X
ami Uqba ibn Nafi 836 Kairoun, Tunisia X
Great Mosque of Susa c. 850 Susa, Tunisia X
Small mosque with graveyard c. 850 Houmt Souk, Tunisia X
Great Mosque of Sfax 850 Sfax, Morocco X
University of al-Qarawiyyin 859 Fez, Morocco X
Mosque with Three Doors 866 Kairoun, Tunisia X
Grand Mosque of Mahdia 916 Mahdia, Tunisia X X
Medjez el-Bab 944 Beja, Tunisia X X
Grand Mosque of Sale 1028 Sale, Morocco X X
Grand Mosque of Tangier 1196 Tangier, Morocco X X
Al-Muwaqqar graveyard 723 Muwaqqar, Jordan X
Qasr el-Bai’j 410 Jordan desert X
Harat Great Mosque 1200 Harat, Afghanistan X
Abdul Qader Yagouri Mosque c. 750 Bini Abbas, Algeria X X
Qasr Hallabat 827
ordan desert X
Masjid I Jami, Mosque of Fahraj c. 850 Fahraj, Iran X
Code: A = Original foundation/qibla could not be determined; B = Qibla appears to roughly parallel
the line from Petra to Mecca or the line of the long axis of the Ka’ba; C = Azimuth information
missing; D = Date of construction before 622 C.E.; E = Date of construction after 900 C.E.; F = Reported
data probably incorrect; G = Most likely qibla direction in error by more than 20 degrees.
Table 2. Mosque/Site data used in analyses (N = 60).
(CE) Location Original
Petra (J) 0.26 75.01 1.65 37.64
Mosque 637 Hama, Syria 193.87
Petra 0.61 25.81 −7.17 13.21
Amr ibn Al-as 642 Fustat, Egypt 90.00
Petra 6.10 −46.00 28.30 19.95
Petra 10.80 −114.40 31.20 51.80
Church ~650 Bethlehem,
Petra 1.90 16.90 147.70 9.30
Mosque ~650 Amman,
Petra −0.30 35.10 −63.30 17.40
Petra 5.02 35.20 −31.80 20.10
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Mosque ~650 Desert Castle,
Petra −4.10 40.60 −65.10 18.25
(Left) ~650 Zeila, Somalia
Petra (J) −0.60 −2.20 −1.80 0.80
Dome of the
Chain 690 Jerusalem 172.03
Petra −1.00 14.70 −94.50 6.85
Qasr Humeima 699 Humeima,
Petra 8.50 −133.02 23.58 −82.9
Mosque 705 San’a, Yemen 333.60
Petra 0.36 7.40 −1.47 3.52
Minya 706 Khirbat al
Petra 0.80 22.14 −10.58 11.47
Hajjaj Mosque 706 Wasit, Iraq 234.98
P/M −26.5 25.3 −35.4 0.60
Khana 708 Damghan,
Mosque 709 Jerusalem 169.61
Petra −3.43 12.31 −179.8 4.44
12.5 −30.53 1.75
P/M −13.2 20.7 −72.1 7.7
al-Kharana 710 Desert Castle,
−37.30 12.10 −98.00
al-Zabib 712 Qatrana,
P/M −33.80 11.10 −118.10 −11.35
Mosque 712 Al Zafaran,
Petra 1.20 37.50 −89.50 19.35
al-Mafjar 714 Jericho, Israel 180.03
Petra −0.59 21.51 −61.34 10.46
Mosque 714 Anjar,
Petra 3.61 27.36 −6.17 15.49
715 Aleppo, Syria 178.70
P/M −15.50 8.40 −21.70 3.55
Qasr Qastal 720 Qastal, Jordan 191.74
Petra −5.20 31.20 −81.50 13.00
‘Umar 721 Bosra, Syria 183.63
P/M −18.74 19.45 −51.60 0.36
Muwaqqar 723 Muwaqqar,
P/M −18.20 21.60 −84.60 1.70
Qasr al-Hayr al
Gharbi 726 Hayr al
P/M −13.86 20.27 −27.10 3.21
Mosque 727 Banbhore,
Mecca −22.61 −2.44 −25.55 12.53
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Qasr Hayr al
Sharqi 728 Hayr al
P/M −21.2 15.6 −32.6 2.80
Mecca −35.25 −1.36 −94.10 18.30
Mosque 740 Ba’albeck,
P/M −13.36 12.02 −23.48 0.67
Qasr Bayir 743 Desert Castle,
Mecca −81.60 4.20 −143.20 38.70
Palace 743 Desert Castle,
Petra −4.10 34.32 −78.52 15.10
Qasr Tubah 743 Desert Castle,
Jerusalem 67.40 129.20 0.00 98.30
P/M −13.87 14.52 −20.97 0.33
749 Um el-Jimal,
P/M −21.90 16.60 −60.50 2.65
Um Jimal Later
749 Um Jimal,
Petra 1.10 39.60 −37.60 24.5
749 Kufa, Iraq 195
Mecca −65.0 −6.0 −75.0 −29
Qasr Aseikhin ~750 Desert Castle,
Mecca −55.20 −1.70 −100.00 −28.45
Al-Fudayn ~750 Mufraq,
P/M −19.90 15.50 −57.30 2.20
Qasr ain as-Sil ~750 Azrak, Jordan 180.30
P/M −37.60 15.30 −85.30 11.15
Mosque ~750 Azraq, Jordan 184.81
P/M −33.00 19.90 −81.30 6.55
Um Jimal Later
Petra 1.10 39.60 −37.60 20.21
Qaisaqiya ~750 Erbil, Iraq 218.53
P/M −14.60 23.50 −22.80 4.45
~750 Erbil, Iraq 234.35
Petra 1.20 39.40 −7.00 20.30
Mosque ~750 Yamama,
P/M −22.30 30.70 −27.60 4.20
~750 Ibra, Oman
Petra −1.20 24.60 −4.80 11.70
Mosque ~750 Guangzhou,
P/M −3.30 7.10 −4.90 1.90
Bibi Samarkan ~750 Samarkan,
Petra (J) 1.78 21.86 −1.23 11.82
Sahi Ramdah ~750 Bowshar, 292.79 −0.58 26.19 −4.24 12.81
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Mosque Oman Petra 7.5
Mansur 762 Baghdad, Iraq 200.03
Mecca −51.10 0.00 −61.30 25.94
Qasr Ukhaydir 764 Kufa, Iraq 198.24
Raqqa Mosque 772 Raqqa, Syria 193.90
P/M −15.17 16.89 −24.12 0.86
827 Desert Castle,
Mecca −40.00 0.70 −88.00 19.65
of Samarra 847 Samarra, Iraq 197.79
Mecca −46.01 1.13 −56.10 22.44
Mecca −24.20 −3.20 −27.40 −13.70
Mosque ~850 Ansaq, Iraq 207.11
Mecca −27.82 4.15 −33.77 −11.83
Mecca −26.34 −5.33 −29.2 −15.83
Mosque 859 Samarra, Iraq 191.57
Mecca −51.02 −4.60 −61.02 −27.81
Mosque 876 Cairo, Egypt 145.40
Mecca 61.21 9.27
9.3 83.51 35.24
Petra = qibla appears to point towards Petra; Mecca = qibla appears to point towards Mecca;
Jerusalem = qibla appears to point towards Jerusalem; P/M = qibla appears to be a location between
Petra and Mecca. A secondary letter such as (J), (B), or (P) indicates that a second city might be close
to the same qibla direction as the first city mentioned. Where two sets of numbers are provided, this
indicates that Gibson seems to have changed the values, the most recent being the added ones,
usually from his website rather than his books. We used the more recent numbers for our statistical
analyses, on the presumption they would be more likely to be correct.
When random, as opposed to systematic, error is involved, measurements of target variables
tend towards normal distributions, centered on a sample mean score. In the case of qiblas, the mean
score should be near zero, with a nearly even division of lower (negative) or higher (positive) angles,
as can be assessed by a one sample t-test or a chi-square test with one degree of freedom. Whether a
distribution is normal or approximately normal can be determined by inspection of its histogram or
by a Kolmogorov-Smirnov one-sample test. A one sample t-test can be used to determine if the mean
score differs significantly from zero, where zero would represent an entirely accurate qibla direction.
As a practical method of assessing accuracy, I wanted to determine what percentage of mosques or
other structures would have qiblas with an accuracy of ± 2, 3, or 5 degrees. Using such a tight
requirement was risky; Ilci et al. (2018) found that mosques built between 1300 and 1660 in part of
northern Turkey had qibla errors from 6 to 18 degrees. SPSS version 26 was used for all statistical
1. The average direction of prayer. The null hypothesis is that the average direction of prayer will
be centered on zero, as assessed by a one sample t-test and a chi-square test with one degree of
freedom. If the null hypothesis is rejected, that might suggest a greater inaccuracy in qibla
determination, with some type of systematic, rather than merely random, bias.
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2. The distribution of qiblas around their mean will be normally distributed by inspection and/or
a test for non-normality, specifically a Kolmogorov-Smirnov one sample test of normality.
3. The limits of 2, 3, and 5 degrees, plus or minus, were considered. My thinking was that if qiblas
could be determined at those levels of accuracy, then ancient architects could probably
distinguish between adjacent cities as long as those cities were several degrees apart in terms of
their azimuths; otherwise, azimuths might not be distinguishable.
4. Qibla accuracy and distance from holy city. The null hypothesis was that there would be no
association between the qibla accuracy and distance from the holy city, tested with a Pearson
zero-order correlation coefficient and a nonparametric Spearman rho correlation coefficient. I
did not have a prediction here of the outcome.
5. Qibla accuracy and approximate date of construction. The null hypothesis was that there would
be no association between the qibla accuracy and the approximate time of construction of the
buildings, tested with a Pearson zero-order correlation coefficient and a Spearman rho
correlation coefficient. I was not sure if the qibla accuracy would improve or decline over time. I
also planned to correlate the date of construction with the distance from the target city, which
was expected to be positive on average.
5.1. Under Gibson’s Assumptions.
Here we assume that the qibla changed from Petra to Mecca, generally in accordance with
1st Hypothesis, Direction of Prayer. The mean score for the 60 qiblas was 0.156 of a degree error,
with a standard deviation of 4.07 degrees of error and a standard error of 0.526 degrees of error. The
median was 0.050 of a degree of error. Using bootstrap methods with 1000 samples, 95% confidence
intervals of −0.87 to 1.22 degrees of error for the mean, −0.80 to 0.90 degrees of error for the median,
and 3.27 to 4.76 degrees of error for the standard deviation were obtained. The one sample t-test
value was 0.297 for 59 degrees of freedom, p = 0.768. The one sample chi-square value for one degree
of freedom, to check whether there were equal numbers of errors on either side of zero, was 0.000, p
= 1.00. Using a one sample Wilcoxin Signed Rank Test to compare the actual data to a median of zero
yielded non-significant results (p = 0.908). All three tests results indicated that the average qibla error
was very close to zero, with an even number of errors on either side of zero.
2nd Hypothesis, Normal Distribution. While the Kolmogorov-Smirnov one-sample test yielded
a significant result (p = 0.013), an inspection of Figure 1 suggests that the actual distribution was
mound-shaped and approximately normally distributed, except that a higher than expected number
of scores occurred near the zero qibla error, reflecting a higher degree of kurtosis. By contrast, the
same K-S test against a uniform distribution yielded a far more significant result (p < 0.005), rejecting
the null hypothesis that the distribution was of a uniform shape. In other words, the violation of
normality was likely due to a greater than expected accuracy rather than higher rates of inaccuracy,
which would have favored more of a uniform distribution.
3rd Hypothesis, Percentages of Accuracy. Over half (51.7%) of the qiblas were within plus or
minus two degrees of accuracy; 61.7% were within three degrees of accuracy; and 81.7% were within
five degrees of accuracy. Over a quarter of the qiblas (26.7%) were within one degree of accuracy.
While some qiblas were more accurate than others, such results do not seem to fit the premise that
early Muslim architects were incapable of determining reasonably accurate qiblas.
4th Hypothesis, Qibla Accuracy and Distance. The zero-order correlation between the distance
from the target city and the error of the qibla was r = −0.116 (p = 0.376). The results for the
nonparametric Spearman rho were similar, rho = −0.125 (p = 0.340). There was a non-significant trend
for the qibla error to be lower (i.e., greater accuracy) with greater distances; perhaps, greater care
was taken for mosques built farther from their direction of prayer.
5th Hypothesis, Qibla Accuracy and Date of Construction. The zero-order correlation between
the date of construction and qibla error was r = −.123 (p = 0.348), as was the Spearman rho (−0.126, p =
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0.339). There was a non-significant trend for the qibla accuracy (i.e., lower error) to improve over
historical time. The distance and date were correlated positively with r = 0.258 (p < 0.05), although
the Spearman rho was much larger, 0.456 (p < 0.001), which may reflect the expansion of Islamic
influence over historical time.
Figure 1. Histogram with normal curve overlay for the degrees of error in early Islamic qiblas.
5.2. Under King’s Assumptions.
Here we assume that the qibla did not change and was always Mecca from 632 C. E. onward.
We did not try to test the hypothesis that the qibla began toward Jerusalem and then was changed,
before Muhammad’s death (c. 632 C.E.), to Mecca (Saifullah et al, 2001).
1st Hypothesis, Direction of Prayer. The mean score for the 60 qiblas was 13.03 of a degree error,
with a standard deviation of 33.93 degrees of error and a standard error of 4.38 degrees of error. The
median was 15.55 degrees of error. Using bootstrap methods with 1000 samples, 95% confidence
intervals were obtained of 4.05 to 21.11 degrees of error for the mean, 12.02 to 20.70 degrees of error
for the median, and 16.68 to 47.25 degrees of error for the standard deviation. The one sample t-test
value was 2.97 for 59 degrees of freedom, p = 0.004. The one sample chi-square value for one degree
of freedom, to check whether there were equal numbers of errors on either side of zero, was 21.60, p
< 0.001. Using a one sample Wilcoxin Signed Rank Test to compare the actual data to a median of
zero yielded significant results (p < 0.001). All three test results indicated that the average qibla error
was significantly different from zero under the King assumption.
2nd Hypothesis, Normal Distribution. While the Kolmogorov-Smirnov one-sample test yielded
a significant result (p = 0.001), the inspected results were similar to those in Figure 1 inasmuch as the
actual distribution was mound-shaped and approximately normally distributed, except that a higher
than expected number of scores occurred near the zero qibla error, reflecting a higher degree of
kurtosis; however, there were also larger outliers than those found in Figure 1. By contrast, the same
K-S test against a uniform distribution yielded equally significant results (p < 0.001), rejecting the
null hypothesis that the distribution was of a uniform shape. In other words, the violation of
normality was likely due to a greater than expected accuracy for a few mosques but also to rather
large outliers at both extremes of the distribution.
Religions 2020, 11, 102 11 of 15
3rd Hypothesis, Percentages of Accuracy. Few (10.0%) of the qiblas were within plus or minus
two degrees of accuracy; 13.3% were within three degrees of accuracy; 20.0% were within five
degrees of accuracy. Only 5% of the qiblas were within one degree of accuracy. Only when larger
ranges of degrees of accuracy were considered, did the percentages increase (±20 degrees, 55.0%; ±30
degrees, 76.7%; ±40 degrees, 90.0%; ±50 degrees, 93.3%; and ±100 degrees, 95.0%). Thus, aside from
Gibson’s contrary thesis, it would indeed appear that King and his supporters were correct in that
the qiblas towards Mecca would not have appeared to have been very accurate.
4th Hypothesis, Qibla Accuracy and Distance. The zero-order correlation between the distance
from the target city and the error of the qibla was r = −0.042 (p = 0.748). The results for the
nonparametric Spearman rho were far stronger, rho = −0.404 (p = 0.001). Overall, the results were
5th Hypothesis, Qibla Accuracy and Date of Construction. The zero-order correlation between
the date of construction and qibla error was r = −0.019 (p = 0.885), while the Spearman rho was −0.245
(p = 0.059). While the results were mixed, there seemed to be a non-significant trend for the qibla
accuracy to improve over historical time. The distance and date were correlated similarly to before,
since the same data and variables were being used.
6. Attempting a Synthesis with Independent Data
Thus far, we have a dilemma. From Gibson’s perspective, qiblas appear to be reasonably
accurate. From King’s perspective, qiblas do not appear to be very accurate, which agrees with his
(King’s) position. That is to say that the data would support both Gibson and King, if we accept their
initial assumptions. A good scholar will look for disconfirming evidence of his or her pet ideas in
order to avoid being a victim of confirmation bias (Schumm 2015), a bias whereby scholars tend to
focus on results that fit their preconceived notions. Two possibilities emerged for testing qibla
accuracy in a way that might synthesize the results of the competing assumptions.
Avni Data. First, I came across a report by Avni (1994) that listed qiblas of a dozen mosques in
the Negev, near the border of Egypt. The qibla azimuths ranged between 158 and 182 degrees, with a
mean of 167.75 and a standard deviation of 5.85. Coins and artifacts dated these sites to the middle of
the seventh century, and probably no earlier than 700 CE. The azimuths clearly do not point toward
Petra, which is to the east southeast, but they do generally point toward Mecca, though often
missing it to the west, aiming closer to due south than the more correct south southeast direction
(However, only a couple were aimed within 5 degrees of due south). One might have hoped that this
data would have served as an excellent test of the two theories, but Gibson himself reports that some
mosques had Meccan qiblas by the early to mid-700s. Some of the mosques in Avni (1994) appear
from his photos to be little more than a single layer of rocks on open ground, and it stretches
credulity to think such structures would have remained completely undisturbed for over 1300 years
or that their qiblas would have been sighted by highly trained Islamic architects. The standard
deviation of the azimuths is a bit larger than that of our findings, which may reflect positioning by
Muslims with lower levels of training in qibla positioning. The two standard deviations can be
compared statistically using an F-test with 11.59 degrees of freedom for which the critical value
(alpha = 0.05) was 1.96. The actual F value was 2.07 (p < 0.038), which indicates that the two standard
deviations are significantly different, as might be expected if architects of large mosques were more
highly trained than those who built lesser structures in more remote areas. Thus, it seems that more
accurate qiblas were obtained by architects who were working on larger structures compared to
those who built far smaller structures in more remote areas. However, though the data here are
limited, they suggest that early mosques aimed towards Mecca were relatively accurate, supporting
Gibson data. Second, in response to questions raised by a reviewer of this report, I narrowed
down the number of mosques under consideration. Gibson, among the 60 mosques in this study,
featured 14 mosques or other structures that he (Gibson) agreed faced Mecca. Presumably, King
would also agree that they faced Mecca. Given contrarian positions on qibla development over the
early Islamic centuries, here we have a potential area of agreement that might allow for a critical test
Religions 2020, 11, 102 12 of 15
and for a synthesis of the competing theories. If these mosques had relatively accurate qiblas, then it
would appear that it was possible that most of the mosques did – suggesting the Gibson was more
correct; if these mosques did not have accurate qiblas, then it would appear that perhaps few of the
mosques had accurate qiblas—and King would be more correct. For these 14 mosques, the mean,
median, standard deviation, and standard error were −0.341, −0.680, 4.184, and 1.118, respectively.
Using bootstrap methods with 1000 samples, 95% confidence intervals were obtained of -2.46 to 1.76
degrees of error for the mean, −3.20 to 1.13 degrees of error for the median, and 2.33 to 5.50 degrees
of error for the standard deviation. The one sample t-test value was −0.305 for 13 degrees of freedom,
p = 0.765. The one sample chi-square value for one degree of freedom, to check whether there were
equal numbers of errors on either side of zero, was 0.286, p = 0.593. Using a one sample Wilcoxin
Signed Rank Test to compare the actual data to a median of zero yielded significant results (p =
0.507). Although the non-significant results may reflect the small sample size and low statistical
power, neither of the Kolmogorov-Smirnov tests for normal or uniform distributions were
significant. 42.9% of the qiblas were within plus or minus two degrees of error; 50.0% were within
three degrees of error, with 78.6% and 100.0% being within five and ten degrees of error,
respectively. 21.4% were within ± one degree of error. None of the correlations among qibla error,
distance, or date were statistically significant in this small sample of mosques. Despite the small
sample, among the 14 mosques, qibla accuracy was fairly good, with non-significant differences
from normal distributions and with central tendencies bracketing zero. The results of our two
follow-up analyses, limited to the accuracy of mosques presumably facing towards Mecca, found
that accuracy was relatively good, in support of Gibson’s thesis and contrary to King’s antithesis.
7. Further Critical Testing
A counter argument could be made against the Gibson hypothesis. Perhaps it should be no
surprise that Meccan qiblas were accurate, but perhaps other qiblas were not, if limited to the same
range of years as the Meccan-oriented mosques. Therefore, our data were limited to non-Meccan
qiblas after the year 726 C.E. to test this alternative explanation. Eighteen mosque qiblas were
analyzed. For these 18 mosques, the mean, median, standard deviation, and standard error were
−0.894, −0.290, 2.778, and 0.655, respectively. Using bootstrap methods with 1000 samples, 95%
confidence intervals were obtained of −2.25 to 0.262 degrees of error for the mean, −1.500 to 1.199
degrees of error for the median, and 1.385 to 3.996 degrees of error for the standard deviation. The
one sample t-test value was -1.366 for 17 degrees of freedom, p = 0.190. The one sample chi-square
value for one degree of freedom, to check whether there were equal numbers of errors on either side
of zero, was 0.222, p = 0.637. Using a one sample Wilcoxin Signed Rank Test to compare the actual
data to a median of zero yielded significant results (p = 0.507, remarkably the same p level as for the
14 mosques). Although the non-significant results may reflect the small sample size and low
statistical power, the Kolmogorov-Smirnov test for a normal distribution was not significant (p =
0.080), while the test against a uniform distribution was significant (p < 0.001). 77.8% of the qiblas
were within plus or minus two (and three) degrees of error, with 94.4% and 100.0% being within five
and ten degrees of error, respectively. 33.3% were within ± one degree of error. None of the
correlations among qibla error, distance, or date were statistically significant in this small sample of
mosques, except for the Spearman nonparametric correlation between the date and distance, rho =
541, p = 0.020. Comparing the qibla error scores for the 14 Meccan-oriented mosques and the 18
other-oriented mosques yielded non-significant results across the two groups, with t(30) = -0.449 (p =
0.657, two-tailed, Cohen’s d = 0.16, less than a “small” effect size per Cohen, 1992) and a
Mann-Whitney U test = 118.50 (p = 0.779, two-tailed exact). The standard deviations of the two
groups were not significantly different either, F(13, 17) = 2.27 (p < 0.058). Thus, there did not appear
to be statistically significant differences in the means or standard deviations as a function of the
different apparent qibla directions. In other words, the qibla accuracy did not vary significantly as a
function of Meccan or non-Meccan orientations.
Religions 2020, 11, 102 13 of 15
On average, under Gibson’s assumptions, the mosque qiblas appeared to be accurate a majority
of the time, within two degrees of azimuth, and nearly always within ten degrees, better than had
been expected. Cohen (1992) set a standard in social science that half a standard deviation was an
effect large enough to detect with the naked eye, which, in this case, would be about two degrees of
azimuth, roughly the width of a human finger extended at arm’s length. The results were balanced
with no significant differences in the number of errors on either side of zero. The results for the qibla
error were approximately normal in appearance, except that a higher percentage of results were
closer to zero than would have been expected for a normal distribution. Although the results were
significant in terms of rejecting the hypothesis that the results were exactly normal, that result
combined with a higher percentage of near misses than would be expected under normal conditions
probably strengthens our results, rather than detracting from them. Greater distances did not seem
to lead to greater qibla errors. As might be expected with the expansion of Islamic influence in the
first two centuries after Muhammad, a strong association was found between more recently
constructed mosques and further distances. Qibla accuracy seemed to increase for more recently
built mosques, a finding that merits further research to determine if technology had improved or if a
greater certainty about qibla directions had a positive effect on accuracy.
Under King’s assumptions, many of the mosques did not appear to have accurate qiblas, in
agreement with King’s assertions. His observations are correct, given his assumption; yet, when
agreement between King and Gibson might be expected—for mosques aimed towards Mecca—the
results suggested fairly high levels of qibla accuracy. That is, when we limited the analyses to
mosques that all would probably agree were oriented towards Mecca, high levels of qibla accuracy
were obtained, suggesting that accuracy might have been possible for qiblas facing different sites
other than Mecca itself. When the latter hypothesis was tested for the other 18 mosques built about
the same time as the 14 Meccan-oriented mosques, no significant differences were found in the qibla
accuracy; other parameters of general qibla accuracy were similar across both groups.
The results here are limited by their reliance upon data provided by Dan Gibson. As he
continues to add new sites to his website, any given analysis of data on an earlier date may become
outdated, even though our data reflected his website’s content as of early February 2020. Our
discussion has not attempted to explain how ancient Islamic architects determined directions from
one location to another. I did not find any evidence that Gibson was making up his results apart
from actual geographic measurements or real data, as have some recent scholars (Schumm,
Crawford, and Lockett 2019a, b). I have had email discussions with Mr. Gibson in an attempt to
clarify some discrepancies found between the data reported in his books and that reported on his
website. If my statistics are in error, I hope that others, including Dr. King, who admits to his own
“distinct penchant with respect to statistics” (2018, p. 18), will correct us, especially if “statistics are
on my [his] side this time” (p. 18).
If one were to try to determine which of two adjacent cities were targets if the angle between
them was smaller than two degrees, I think it would be a challenge to distinguish between them, as
the difference would be only about one half a standard deviation, although it might have to be done
in conjunction with other available information (e.g., date of construction) or associated historical
events. If the angles were different by more than four degrees, making distinctions would be more
certain because that difference would represent about one standard deviation or more. For example,
suppose the true qibla to Mecca was 160 degrees but the mosque was aimed due south (180 degrees).
Our results would suggest that it was more likely, from a statistical perspective, that the architects
intended the qibla to be due south, for whatever reason, rather than aimed to face Mecca. If, on the
other hand, the mosque was aimed at 158 degrees, that would probably mean the intended qibla was
Religions 2020, 11, 102 14 of 15
either Mecca or an attempt to parallel the long axis of the Ka’ba, despite the small error. If the error
was more than four to eight degrees, the alignment may have been set up by mistake or based, at
least partly, on some other criterion. However, if the objective is to compare groups of qiblas, then the
standard error becomes more relevant and differences of as little as one or two degrees might
represent a statistically significant difference.
In spite of the limitations of this study, the results found here appear to indicate that qiblas
could be determined with a fair degree of accuracy in the first two or three centuries of Islam,
regardless of the apparent sites faced by the mosques. At the same time, King’s observations that,
assuming Mecca to be the only qibla, qiblas could not be determined with much accuracy, are
factually correct if one accepts his assumption. However, we found that, when assessing only
mosques regarding which both sides would agree should have qiblas towards Mecca, qiblas were
relatively accurate, though not perfect. We also found that qiblas in other directions than Mecca had
similar degrees of accuracy as those known to have been towards Mecca at about the same historical
time. Thus, overall, it appears that most mosques in the first two centuries of Islam could have had a
fairly high degree of qibla accuracy, maybe even higher than mosques in far more recent centuries
(Ilci et al. 2018). How early Islamic architects were able to obtain high rates of qibla accuracy remains
to be determined but also remains an interesting question. Now, knowing that they did have high
rates of accuracy, this has surely become a reasonable question for further inquiry. Furthermore, a
related question would be explaining how some Islamic architects were able to achieve qibla
accuracies of plus or minus one or two degrees, while others erred by ten or more degrees. Were
these different architects using different methods for determining the qibla direction? If so, how or
why were their methods different? Were the architects using the same method but some with fewer
mistakes, or were the architects using very different methods, with some methods being more
accurate than others?
Funding: No funding from any source was used to support this research.
Acknowledgments: My appreciation is expressed to Dan Gibson and Zvi Goldman for their helpful comments
on earlier drafts of this manuscript, as well as to two anonymous reviewers who encouraged a deeper analysis
of the data. Dan Gibson deserves even more appreciation for making his data publicly available for
independent study and analysis and for his personal courage in tackling potentially sensitive research issues.
Conflicts of Interest: The author declares no conflict of interest. The author is a substitute pastor at a
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